I had this problem also and I found a solution after hard work, so you pay me 500€ I'll tell you the solution- just joking, here it is (Win10):
1) Go to C:\Users\<YOUREUSERNAME>\AppData\Roaming\Natural Selection 2\
2) Delete all Files or drop it in a new Folder called "Backup".
3) Start the Game and new Files will be created, connecting will work again.
4) Now I'm your hero, play with me on "IBISGamin.com NS2#1 NY (Noob Friendly)", I'm Shimon.

Also you can play an check wich one of the files is the corrupt one by replacing the new (good one) one by one with the old one and write it here.

This happened to me after playing alonone against Bots on an empty server wich had one map playing for a very long time, after that server I connected another and it took a very long time with black screen, after that it told me "connection time out" (if any dev is reading this).

Admin get this into the FAQ or pin my Answer.

This didn't work for me and I was ready to call you my hero.